Virtual beam steering using MIMO radar

ABSTRACT

Examples disclosed herein relate to a Multiple-Input Multiple-Output (MIMO) radar for virtual beam steering. The MIMO radar has a plurality of transmit antennas and a receive antenna array having a plurality of radiating elements. The MIMO radar also includes a digital signal processor (DSP) configured to synthesize a virtual receive array having N×M receive subarrays from the plurality of transmit antennas and the receive antenna array, where N is the number of transmit antennas and M is the number of receiving elements. Other examples disclosed herein relate to a method of virtual beam steering.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional Application No.62/684,859, filed on Jun. 14, 2018, and incorporated by reference in itsentirety.

BACKGROUND

Multiple Input, Multiple Output (“MIMO”) radar technology has emerged asa leading contender for advanced communication systems, including thosebeing designed for millimeter wave applications in the 30 GHz to 300 GHzfrequency spectrum. A MIMO radar employs multiple transmit antennas andhas the ability to jointly process signals received at multiple receiveantennas. Each transmit antenna transmits an independent waveform, whichenables the MIMO radar to exploit increased degrees of freedom at thetransmit array to improve resolution, flexibility, and adaptivity incomparison to conventional phase-array systems. Phase-array systemsalready possess several advantages over classical radar antennas basedon their mechanical steering abilities with a wide Field-of-View(“FoV”). One of their shortcomings, however, is the degraded performanceof phased-arrays when beams are steered to large angles. Not only is theantenna gain reduced significantly, but also the beam width isbroadened. As a result, the FoV within which beam steering is performedwith phase-array systems is usually limited to −120° to 120°.

During the last years new array antenna designs have been proposed anddeveloped, including virtualization of radiating elements in receivemode. There have been several different ways to create virtual arraysand the main such techniques can be in two categories. The first oneconsists of creating duplicated receiver arrays using specificallyplaced multiple transmit antennas in MIMO configurations, which is alsoknown as active virtual arrays. The second one, referred to as passivevirtual arrays, create virtual receive arrays using a pair or multiplereceiving antenna elements according to a specific geometry. In thiscategory, a highly useful technique is to create virtual arrays fromphysical receive arrays using interpolation.

BRIEF DESCRIPTION OF THE DRAWINGS

The present application may be more fully appreciated in connection withthe following detailed description taken in conjunction with theaccompanying drawings, in which like reference characters refer to likeparts throughout, and in which:

FIG. 1 illustrates a schematic diagram of a virtual antenna array in aMIMO configuration in accordance with various examples of the subjecttechnology;

FIG. 2 illustrates a schematic diagram of a virtual antenna array in aMIMO configuration where a linear transformation is performed on themanifold matrix in accordance with various examples of the subjecttechnology;

FIG. 3 illustrates a schematic diagram of a virtual antenna array wherean oriented subarray is formed by interpolation in accordance withvarious examples of the subject technology;

FIG. 4 illustrates a flowchart for creating virtual beam steering usinga MIMO radar configuration in accordance with various examples of thesubject technology;

FIG. 5 illustrates a diagram of a MIMO radar system in accordance withvarious examples of the subject technology;

FIG. 6 conceptually illustrates an example receive array for use withthe MIMO radar system of FIG. 5 in accordance with various examples ofthe subject technology;

FIG. 7 illustrates plot diagrams of array geometries for different MIMOradar configurations in accordance with various examples of the subjecttechnology;

FIG. 8 conceptually illustrates an example of a reconfigurable physicaltransmit array with different MIMO radar configurations in accordancewith various examples of the subject technology;

FIG. 9 conceptually illustrates an example of a reconfigurable physicalreceive array with different MIMO radar configurations in accordancewith various examples of the subject technology;

FIG. 10 conceptually illustrates a flow chart of an example MIMO signalprocess based on a virtual receive array geometry in accordance withvarious examples of the subject technology;

FIG. 11 conceptually illustrates an example of a reconfigurable physicaltransmit array with a particular MIMO radar configuration in accordancewith various examples of the subject technology; and

FIG. 12 conceptually illustrates an example of a switch network for areconfigurable physical receive array in accordance with variousexamples of the subject technology.

DETAILED DESCRIPTION

Virtual beam steering using MIMO radar is disclosed herein. The radar issuitable for many different applications and can be deployed in avariety of different environments and configurations. In variousexamples, the radar is used in an autonomous driving vehicle to detectand identify targets in the vehicle's path and surrounding environment.The targets may include structural elements in the environment such asroads, walls, buildings, road center medians and other objects, as wellas vehicles, pedestrians, bystanders, cyclists, plants, trees, animalsand so on.

The detailed description set forth below is intended as a description ofvarious configurations of the subject technology and is not intended torepresent the only configurations in which the subject technology may bepracticed. The appended drawings are incorporated herein and constitutea part of the detailed description. The detailed description includesspecific details for the purpose of providing a thorough understandingof the subject technology. However, the subject technology is notlimited to the specific details set forth herein and may be practicedusing one or more implementations. In one or more instances, structuresand components are shown in block diagram form in order to avoidobscuring the concepts of the subject technology. In other instances,well-known methods and structures may not be described in detail toavoid unnecessarily obscuring the description of the examples. Also, theexamples may be used in combination with each other.

FIG. 1 is a schematic diagram of a virtual antenna array in a MIMOconfiguration in accordance with various examples. Not all of thedepicted components may be used, however, and one or moreimplementations may include additional components not shown in thefigure. Variations in the arrangement and type of the components may bemade without departing from the scope of the claims set forth herein.Additional components, different components, or fewer components may beprovided.

Virtual antenna array 100 has multiple transmit antennas 102-106 and aphysical receive array 108. Each transmit antenna is positioned at agiven set of coordinates (x,y,z), such as (x₁,y₁,z₁) for transmitantenna T_(x)(1) 102. The transmit antennas are spaced within a relativedistance of each other, e.g., distance d₁₂ between transmit antennas 102and 104, and have an omnidirectional transmit pattern, or a specificbeam pattern. In this MIMO configuration, the signals from each transmitantenna 102-106 are mutually orthogonal.

The physical receive array 108 is a two-dimensional (2D) array designedwith a number of radiating elements. In the example shown, the physicalreceive array 108 has 24 radiating elements (e.g., radiating element110). The radiating elements may be antennas of different types,geometries and configurations, depending on the application and desiredradiation characteristics, gain, feeding mechanism, polarization,bandwidth, and size. The spacing between each radiating element issmaller than the wavelength such that grating lobes immunity isachieved. The size of the physical receive array 108 is designed so thata satisfactory system level trade-off can be achieved betweenperformance (e.g., signal-to-noise ratio) and processing complexity andspeed.

Note that the multiple transmit antennas 102-106 and the physicalreceive array 108 synthesize a virtual antenna array 100 having N×Mreceive arrays, where N is the number of transmit antennas and M is thenumber of receiving elements. In one example, there are 72 virtualreceiving elements for the 3 transmit antennas 102-106 and 24 radiatingelements in the physical receive array 108, forming virtual receivearrays 112-114. The virtual receive arrays 112-114 are spaced by thesame distance d₁₂ between transmit antennas 102 and 104. Note also thatthe virtual antenna array 100 may be represented by complex manifoldmatrix 116. Manifold matrix A 116 is a function of the geometry of thearray, the carrier frequency and the Direction of Arrival (“DoA”) of thetransmit antennas.

By using sophisticated digital signal processing on virtual antennaarray 100, it is possible to steer the receive beam without activedevices such as phase shifters and time delay lines, thereby alleviatingthe hardware complexity by a large amount.

FIG. 2 illustrates a schematic diagram of a virtual antenna array 200 ina MIMO configuration where a linear transformation is performed on themanifold matrix in accordance with various examples of the subjecttechnology. Virtual antenna array 200 is generated by applying a lineartransformation to the manifold matrix A 116 using interpolation. In oneexample, applying the linear transformation H to transmit antennas202-206 results in transmit antennas 202, 216 and 218 positioned at anangle relative to transmit antennas' original placement. Similarly, thelinear transformation results in receive arrays 208, 220 and 222, alsoat an angle from their original placement. The resulting receive arrays208, 220 and 222 are designed so that their regular spacing and shapefacilitate the subsequent Digital Signal Processing (“DSP”) for DoAs andhigh level beamforming.

The linear transformation matrix His calculated under an optimalcriterion, such as least squares, maximum likelihood, and so on. Whenthe size of the virtual arrays is smaller than the physical array, themanifold transform can be calculated by least square algorithms. Incases where a virtual array would be larger than its generating physicalarray, an optimal transform needs to be found by optimization. Duringthis process, precautions can be done to avoid possible grating lobes inreceive beam patterns. The proposed system architecture of virtualantenna array 200 is highly flexible in that various active virtualarray configurations can be obtained by either changing the transmitantennas spacing and relative locations, and/or the shape and size ofthe physical receive array 208.

In some implementations, the manifold matrix can be formed from physicalgeometry of a physical array with the following process. In a MIMO radarsystem, for a receive array, which is a uniform linear array (ULA) withM antenna elements or sensors, and N transmit antennas, the manifoldmatrix can be expressed as follows:

$\begin{matrix}{A = \begin{bmatrix}{g_{11}e^{{- {jw}_{o}}\tau_{11}}} & \ldots & {g_{1N}e^{{- {jw}_{o}}\tau_{1N}}} \\\vdots & \ddots & \vdots \\{g_{M\; 1}e^{{- {jw}_{o}}\tau_{M\; 1}}} & \ldots & {g_{MN}e^{{- {jw}_{o}}\tau_{MN}}}\end{bmatrix}} & {{Eq}.\mspace{14mu}(1)}\end{matrix}$

where {g_(ij)} are the channel responses between the ith transmitantenna to the jth receive antenna element, and {τ_(ij)} are the timedelays between the ith transmit antenna to the jth receive antennaelement, with respect to the reference antenna element, which can be theone located at the phase center of the virtual receive array, for i=1,2, . . . , M and j=1, 2, . . . , N. The time delay τ_(ij) is a functionof the center frequency w_(o), and d_(ij), the distance between the ithelement to the reference element, and also the incident angle θ_(i),which is the angle between the direction of the incident signal receivedat the ith element and the normal, which is perpendicular to the planeof the virtual receive array, which can be expressed as follows:

$\begin{matrix}{\tau_{ij} = {\frac{1}{c}d_{ij}{\sin\left( \theta_{i} \right)}}} & {{Eq}.\mspace{14mu}(2)}\end{matrix}$for i=1, 2, . . . , M and j=1, 2, . . . , N, and c=3×10⁸ m/s is thespeed of light.

Once the array geometry is determined, all the distances between theantenna elements to the reference element of the jth subarray of thevirtual receive array can be determined. For example, the incidentangles may be derived from a predetermined or assumed DoA for each ofthe N subarrays that constitute the virtual receive array.

In some implementations, by selecting geometries for both physicaltransmit array and physical receive array, different, variable andsuitable virtual receive array configurations can be created to meet thebeam steering requirements. Depending on the physical arrayconfigurations in both transmit and receive arrays, virtual receivearray configurations can be created and used for large diversity whilealleviating the beam steering loss.

The linear transformation described herein can be used to construct avirtual receive array. Starting from the system requirements, forexample the FoV, the beam steering angular range can be determined. Theprocess involves dividing the FoV into a subset number of regions, whereeach region corresponds to a pre-rotated angle. For a specific angle, aphysical receive array can be selected with considerations of theperformance and cost, and also in terms of the complexity of the signalprocessing. For a chosen number, N, of the physical transmit antennas,and a chosen number, M, of the physical receive array elements, thecomplexity of signal processing can be determined. A working examplethat presents the process for forming a virtual receive array will bedescribed in more detail in FIGS. 7-10.

Attention is now directed to FIG. 3, which shows a schematic diagram ofa virtual antenna array where an oriented subarray is formed byinterpolation in accordance with various examples. Virtual antenna array300 has a physical receive array 302 as shown in the lower left, with 24radiating elements. Virtual antenna array 300 also has four transmitantennas 304-310. With 4 transmit antennas and a physical receive arraywith 24 radiating elements, 96 virtual receive elements are created invirtual antenna array 300. In one example, all the signals received bythe 96 virtual receive elements are used in interpolation to create theoriented virtual subarray (in blue) 312 at an angle of 0°. In anotherexample, an oriented virtual subarray (in green) 314 is created atanother angle. The resulting virtual subarrays enable phased arrayoperations such as beam steering and field scanning to be performedwithout use, or with reduced use, of phase shifters or time delay lines,with high performance and reduced hardware complexity.

FIG. 4 is a flowchart for creating virtual beam steering using a MIMOradar configuration in accordance with various examples. First, from aMIMO radar configuration with a given number of transmit antennas and aphysical receive array of radiating elements, an active virtual receivearray is formed that is represented by a manifold matrix A (400). Basedon a set of steering angle and performance requirements, an orientedvirtual receive array configuration is specified with a manifold matrixB (402). From the manifold matrices A and B, a transformation matrix Hisdetermined such that B=HA. The linear transformation matrix isdetermined under an optimization criterion such thatH*=arg{Opt[f(A,B)]}=arg {Opt[f(A,HA)]} (404). Lastly, using H* and thereceived signal samples, a data set is formed for further processing,e.g., DoA, beamforming, etc.

FIG. 5 shows a diagram of a MIMO radar system in accordance with variousexamples. MIMO radar system 500 has a virtual antenna array 502 of fourtransmit antennas 504-510, a physical receive array 512 and virtualreceive arrays 514-516. The MIMO radar system 500 also has a DSP unit518 for performing linear transformations on the virtual antenna array500 to create virtual beam steering at any desired angle. As describedabove, this is achieved without the use of phase shifters, time delayelements, and so forth, and at a reduced complexity and performanceimprovement. All that is required to produce flexible virtual beamsteering is a virtual receive array such as array 502 and a DSP unit 518capable of performing the linear transformations on antenna manifolds asdescribed above. Note that the receive arrays in virtual receive array500 have multiple radiating elements which can be of any type andconfiguration.

An example receive array is illustrated in FIG. 6. Receive array 600contains multiple metamaterial (“MTM”) cells positioned in one or morelayers of a substrate and coupled to other circuits, modules and layers,as desired and depending on the application. MTM cell 602 is illustratedhaving a conductive outer portion or loop 604 surrounding a conductivearea 606 with a space in between. Each MTM cell 602 may be configured ona dielectric layer, with the conductive areas and loops provided aroundand between different MTM cells. A voltage controlled variable reactancedevice 608, e.g., a varactor, provides a controlled reactance betweenthe conductive area 606 and the conductive loop 604. The controlledreactance is controlled by an applied voltage, such as an appliedreverse bias voltage in the case of a varactor. The change in reactancechanges the behavior of the MTM cell 602, enabling the MTM array 600 toreceive focused, high gain beams directed to a specific location. It isappreciated that additional circuits, modules and layers may beintegrated with the MTM array 600.

As generally described herein, an MTM cell such as cell 602 is anartificially structured element used to control and manipulate physicalphenomena, such as the electromagnetic (“EM”) properties of a signalincluding its amplitude, phase, and wavelength. Metamaterial structuresbehave as derived from inherent properties of their constituentmaterials, as well as from the geometrical arrangement of thesematerials with size and spacing that are much smaller relative to thescale of spatial variation of typical applications. A metamaterial isnot a tangible new material, but rather is a geometric design of knownmaterials, such as conductors, that behave in a specific way. An MTMcell may be composed of multiple microstrips, gaps, patches, vias, andso forth having a behavior that is the equivalent to a reactanceelement, such as a combination of series capacitors and shunt inductors.Various configurations, shapes, designs and dimensions are used toimplement specific designs and meet specific constraints. In someexamples, the number of dimensional freedom determines thecharacteristics, wherein a device having a number of edges anddiscontinuities may model a specific-type of electrical circuit andbehave in a similar manner. In this way, an MTM cell radiates accordingto its configuration. Changes to the reactance parameters of the MTMcell result in changes to its radiation pattern. Where the radiationpattern is changed to achieve a phase change or phase shift, theresultant structure is a powerful antenna or radar, as small changes tothe MTM cell can result in large changes to the beamform.

The MTM cells include a variety of conductive structures and patterns,such that a received transmission signal is radiated therefrom. Invarious examples, each MTM cell has some unique properties. Theseproperties may include a negative permittivity and permeabilityresulting in a negative refractive index; these structures are commonlyreferred to as left-handed materials (“LHM”). The use of LHM enablesbehavior not achieved in classical structures and materials, includinginteresting effects that may be observed in the propagation ofelectromagnetic waves, or transmission signals. Metamaterials can beused for several interesting devices in microwave and terahertzengineering such as antennas, sensors, matching networks, andreflectors, such as in telecommunications, automotive and vehicular,robotic, biomedical, satellite and other applications. For antennas,metamaterials may be built at scales much smaller than the wavelengthsof transmission signals radiated by the metamaterial. Metamaterialproperties come from the engineered and designed structures rather thanfrom the base material forming the structures. Precise shape,dimensions, geometry, size, orientation, arrangement and so forth resultin the smart properties capable of manipulating EM waves by blocking,absorbing, enhancing, or bending waves.

FIG. 7 illustrates plot diagrams of array geometries for different MIMOradar configurations in accordance with various examples of the subjecttechnology. In FIG. 7, plot diagrams 701-709 depict a physical array(left), a physical transmit array (middle), and a virtual receive array(right) with 3 rotation angles: 0° (top), −45° (middle), and +45°(bottom). As illustrated in FIG. 7, a transmit (T_(x)) array and areceive (R_(x)) array are used. The T_(x) array can be either sparse orspaced by λ/2, and the R_(x) array can also be either sparse or spacedby λ/2. In some implementations, the physical transmit array andphysical receive array consist of 6 elements to support three rotationsof 0°, −45° and +45°.

In some implementations, the azimuth (AZ) orientation angle of 0° can bedefined as boresight, where the orientation angle range of [−90°, 90° ]can be divided into multiple (e.g., three (3)) “subzones-of-sight”:[−90°, −30° ], [−30°, 30°], and [30°, 90° ]. For an AZ range of [−30°,30° ], the pre-rotation angle can be set to 0°, and the receive beamforming can be within a range of [−30°, 30° ]. In some aspects, for apre-rotated angle in AZ of 45° and −45°, and receive beam forming can bewithin a range of [−30°, 30° ]. The constructed virtual receive arraymay have a larger aperture for targets in all the three“subzones-of-sight.”

The left-most plot diagrams of FIG. 7, from top-to-bottom order, depictthree (3) physical receive array configurations, corresponding to 0°,−45° and +45° rotation angles, respectively. For example, the plotdiagram 701 depicts a physical receive array with a rotation angle at0°. The plot diagram 704 depicts the physical receive array with therotation angle at −45°. The plot diagram 707 depicts the physicalreceive array with the rotation angle at +45°. In the plot diagram 704,the condition for grating lobe free is that the spacing “dp” is lessthan λ, in the 6 ULAs.

The middle plot diagrams of FIG. 7, from top-to-bottom order, depictthree (3) physical transmit array configurations, corresponding to 0°,−45° and +45° rotation angles, respectively. For example, the plotdiagram 702 depicts a physical transmit array with the rotation angle at0°. The plot diagram 705 depicts the physical transmit array with therotation angle at −45°. The plot diagram 708 depicts the physicaltransmit array with the rotation angle at +45°. In some aspects, thephysical transmit and receive arrays are both reconfigurable as will bedescribed in FIG. 8 and FIG. 9.

The right-most plot diagrams of FIG. 7, from top-to-bottom order, depictthree (3) virtual receive array configurations, corresponding to 0°,−45° and +45° rotation angles, respectively. For example, the plotdiagram 703 depicts a virtual receive array with the rotation angle at0°. The plot diagram 706 depicts the virtual receive array with therotation angle at −45°. The plot diagram 709 depicts the virtual receivearray with the rotation angle at +45°.

FIG. 8 conceptually illustrates an example of a reconfigurable physicaltransmit array with different MIMO radar configurations in accordancewith various examples of the subject technology. In FIG. 8, a firstconfiguration pattern 802 depicts the reconfigurable physical transmitarray switched to a transmit array with an orientation angle set to−45°, a second configuration pattern 804 depicts the reconfigurablephysical transmit array switched to a transmit array with theorientation angle set to 0°, and a third configuration pattern 806depicts the reconfigurable physical transmit array switched to atransmit array with the orientation angle set to +45°. The firstconfiguration pattern 802 may correspond to the transmit array depictedin the plot diagram 704 of FIG. 7. The second configuration pattern 804may correspond to the transmit array depicted in the plot diagram 701 ofFIG. 7. And the third configuration pattern 806 may correspond to thetransmit array depicted in the plot diagram 707 of FIG. 7.

FIG. 9 conceptually illustrates an example of a reconfigurable physicalreceive array with different MIMO radar configurations in accordancewith various examples of the subject technology. In FIG. 9, a firstconfiguration pattern 902 depicts the reconfigurable physical receivearray switched to a receive array with an orientation angle set to +45°,a second configuration pattern 904 depicts the reconfigurable physicalreceive array switched to a receive array with the orientation angle setto 0°, and a third configuration pattern 906 depicts the reconfigurablephysical receive array switched to a receive array with the orientationangle set to −45°. The first configuration pattern 902 may correspond tothe receive array depicted in the plot diagram 708 of FIG. 7. The secondconfiguration pattern 904 may correspond to the receive array depictedin the plot diagram 702 of FIG. 7. And the third configuration pattern906 may correspond to the receive array depicted in the plot diagram 705of FIG. 7.

In both FIG. 8 and FIG. 9, the different MIMO radar configurations canbe realized by using switches (not shown). For example, in a transmitarray with N signal channels (e.g., N=6), the switches can control Ntransmit antennas in any of the three rotation scenarios (e.g., 0°, −45°and +45° rotation angles). In a case of rotation by −45° and +45°, 6Uniform Receive Arrays (“URAs”) can be used for beamforming and theperformance is enhanced by the diversity gain provided by the enlargedvirtual receive apertures in both rotation scenarios. The enhancementcan compensate for the possible beam steering loss. In the case withoutrotation, 4 virtual URAs can be used for receive beamforming.

FIG. 10 conceptually illustrates a flow chart of an example MIMO signalprocess for beamforming operation using a virtual receive array geometryin accordance with various examples of the subject technology. Not allof the depicted components may be used, however, and one or moreimplementations may include additional components not shown in thefigure. Variations in the arrangement and type of the components may bemade without departing from the scope of the claims set forth herein.Additional components, different components, or fewer components may beprovided.

As illustrated, orthogonal Tx waveforms are received by M MatchedFilters (“MF”) 1008, and then combined at each of the N receivers. Theorthogonality of the Tx waveforms means these waveforms do not interferewith each other when they are passed through their respective MF. Asused herein, a MF encompasses any signal detection in the presence of anumber of orthogonal (or near-orthogonal) and non-orthogonal waveforms.For example, for spectrum spreading waveforms using Pseudo-random Noise(“PN”) sequences having good auto-correlation and cross-correlationproperties, the matched filtering is to perform code correlation andpeak finding processing. For Time-Division Multiple Access (“TDMA”) andFrequency-Division Multiple Access (“FDMA”) orthogonal waveforms, timingcontrol and channelization filtering are used, respectively.

In some implementations, M orthogonal waveforms can be present at eachof the N receive antenna elements 1002. From each receive antennaelement 1002 in the physical receive array, all the M orthogonal signalsare present and down-converted by frequency conversion modules 1004(depicted as “D/C”) and then sampled by Analog-to-Digital Converters(“ADC”) 1006. The obtained digital sample stream is then processed by aMF 1008. In some aspects, the MF 1008 can be a correlator with a localPN code, or a receive filter designed to meet the Nyquist criteria,i.e., inter-symbol interference free with symbol timing. In both cases,decimation is done so that the signals are in symbol level. In someimplementations, signal conditioning functionalities may be implicitlycontained (not shown). The M orthogonal signals are separated andpresent to M phase shifters 1010 (depicted as 4) for phase alignment,and combined coherently with a coherent combining module 1012. Data isthen collected from the outputs from the coherent combining modules 1012with a data collection module 1014. The resulting signals are then usedfor application level processing for range, Doppler and imaging, amongothers, with a processing unit 1016.

FIG. 11 conceptually illustrates an example of a switch network 1110 fora reconfigurable physical transmit array in accordance with variousexamples of the subject technology. The reconfigurable physical transmitarray may be coupled to multiple Single Pole Double Throw (“SPDT”)switches. For example, the reconfigurable physical transmit array may becoupled to two (2) SPDT switches (e.g., 1132 and 1134).

FIG. 11 also depicts a series of input ports 1120 that correspond to thereconfigurable physical transmit array in the switch network 1110, wherea subset of the input ports are coupled to the SPDT switches 1132 and1134. In some implementations, input ports 2 and 5 are coupled to SPDTswitch 1232 and input ports 1 and 4 are coupled to SPDT switch 1234. Forexample, when SPDT switch 1132 takes Input Port 5, and SPDT switch 1134takes Input Port 4, the SPDT switches 1132 and 1134 cause thereconfigurable physical transmit array to switch to a transmit arraywith an orientation angle set to +45°. In another example, when SPDTswitch 1132 takes Input Port 2, and SPDT switch 1134 takes Input Port 4,the SPDT switches 1132 and 1134 cause the reconfigurable physicaltransmit array to switch to a transmit array with an orientation angleset to 0°. In still another example, when SPDT switch 1132 takes InputPort 2, and SPDT switch 1134 takes Input Port 1, the SPDT switches 1132and 1134 cause the reconfigurable physical transmit array to switch to atransmit array with an orientation angle set to −45°.

FIG. 12 conceptually illustrates an example of a switch network 1210 fora reconfigurable physical receive array with a particular MIMO radarconfiguration in accordance with various examples of the subjecttechnology. The reconfigurable physical receive array may be coupled tomultiple SPDT switches. For example, the reconfigurable physical receivearray may be coupled to four (4) SPDT switches (e.g., 1232, 1234, 1236,1238).

FIG. 12 also depicts a series of input ports 1220 that correspond to thereconfigurable physical receive array in the switch network 1210, wherea subset of the input ports are coupled to the SPDT switches 1232, 1234,1236, and 1238. In some implementations, input ports 2 and 7 are coupledto the SPDT switch 1232, input ports 1 and 8 are coupled to the SPDTswitch 1234, input ports 3 and 5 are coupled to the SPDT switch 1236,and input ports 0 and 4 are coupled to the SPDT switch 1238. Forexample, when SPDT switch 1232 takes Input Port 2, SPDT switch 1234takes Input Port 1, SPDT switch 1236 takes Input Port 5, and SPDT 1238switch takes Input Port 0, the SPDT switches 1232, 1234, 1236 and 1238cause the reconfigurable physical receive array to switch to a transmitarray with an orientation angle set to −45°. In another example, whenSPDT switch 1232 takes Input Port 7, SPDT switch 1234 takes Input Port8, SPDT switch 1236 takes Input Port 5, and SPDT switch 1238 takes InputPort 0, the SPDT switches 1232, 1234, 1236 and 1238 cause thereconfigurable physical receive array to switch to a transmit array withan orientation angle set to 0°. In still another example, when SPDTswitch 1232 takes Input Port 7, SPDT switch 1234 takes Input Port 8,SPDT switch 1236 takes Input Port 3, and SPDT switch 1238 takes InputPort 4, the SPDT switches 1232, 1234, 1236 and 1238 cause thereconfigurable physical receive array to switch to a transmit array withan orientation angle set to +45°.

It is appreciated that the previous description of the disclosedexamples is provided to enable any person skilled in the art to make oruse the present disclosure. Various modifications to these examples canbe readily apparent to those skilled in the art, and the genericprinciples defined herein may be applied to other examples withoutdeparting from the spirit or scope of the disclosure. Thus, the presentdisclosure is not intended to be limited to the examples shown hereinbut is to be accorded the widest scope consistent with the principlesand novel features disclosed herein.

As used herein, the phrase “at least one of” preceding a series ofitems, with the terms “and” or “or” to separate any of the items,modifies the list as a whole, rather than each member of the list (i.e.,each item).The phrase “at least one of” does not require selection of atleast one item; rather, the phrase allows a meaning that includes atleast one of any one of the items, and/or at least one of anycombination of the items, and/or at least one of each of the items. Byway of example, the phrases “at least one of A, B, and C” or “at leastone of A, B, or C” each refer to only A, only B, or only C; anycombination of A, B, and C; and/or at least one of each of A, B, and C.

Furthermore, to the extent that the term “include,” “have,” or the likeis used in the description or the claims, such term is intended to beinclusive in a manner similar to the term “comprise” as “comprise” isinterpreted when employed as a transitional word in a claim.

A reference to an element in the singular is not intended to mean “oneand only one” unless specifically stated, but rather “one or more.” Theterm “some” refers to one or more. Underlined and/or italicized headingsand subheadings are used for convenience only, do not limit the subjecttechnology, and are not referred to in connection with theinterpretation of the description of the subject technology. Allstructural and functional equivalents to the elements of the variousconfigurations described throughout this disclosure that are known orlater come to be known to those of ordinary skill in the art areexpressly incorporated herein by reference and intended to beencompassed by the subject technology. Moreover, nothing disclosedherein is intended to be dedicated to the public regardless of whethersuch disclosure is explicitly recited in the above description.

While this specification contains many specifics, these should not beconstrued as limitations on the scope of what may be claimed, but ratheras descriptions of particular implementations of the subject matter.Certain features that are described in this specification in the contextof separate implementations can also be implemented in combination in asingle implementation. Conversely, various features that are describedin the context of a single implementation can also be implemented inmultiple implementations separately or in any suitable sub combination.Moreover, although features may be described above as acting in certaincombinations and even initially claimed as such, one or more featuresfrom a claimed combination can in some cases be excised from thecombination, and the claimed combination may be directed to a subcombination or variation of a sub combination.

The subject matter of this specification has been described in terms ofparticular aspects, but other aspects can be implemented and are withinthe scope of the following claims. For example, while operations aredepicted in the drawings in a particular order, this should not beunderstood as requiring that such operations be performed in theparticular order shown or in sequential order, or that all illustratedoperations be performed, to achieve desirable results. The actionsrecited in the claims can be performed in a different order and stillachieve desirable results. As one example, the processes depicted in theaccompanying figures do not necessarily require the particular ordershown, or sequential order, to achieve desirable results. Moreover, theseparation of various system components in the aspects described aboveshould not be understood as requiring such separation in all aspects,and it should be understood that the described program components andsystems can generally be integrated together in a single hardwareproduct or packaged into multiple hardware products. Other variationsare within the scope of the following claim.

What is claimed is:
 1. A Multiple-Input Multiple-Output (MIMO) radar forvirtual beam steering, comprising: a plurality of transmit antennas; areceive antenna array having a plurality of radiating elements; and adigital signal processor (DSP) configured to synthesize a virtualreceive array having N×M receive subarrays from the plurality oftransmit antennas and the receive antenna array, where N is the numberof transmit antennas and M is the number of receiving elements, andwherein the virtual receive array is represented by a manifold matrixthat is a function of a geometry of the receive antenna array and acarrier frequency and direction of arrival of the plurality of transmitantennas, and the DSP is configured to apply a transformation matrix tothe manifold matrix to generate the virtual receive array.
 2. The MIMOradar of claim 1, wherein the manifold matrix is defined as:${A = \begin{bmatrix}{g_{11}e^{{- {jw}_{o}}\tau_{11}}} & \ldots & {g_{1N}e^{{- {jw}_{o}}\tau_{1N}}} \\\vdots & \ddots & \vdots \\{g_{M\; 1}e^{{- {jw}_{o}}\tau_{M\; 1}}} & \ldots & {g_{MN}e^{{- {jw}_{o}}\tau_{MN}}}\end{bmatrix}},$ where g_(ij) is channel response between i^(th)transmit antenna to j^(th) receive antenna element, w_(o) is a centerfrequency, and τ_(ij) is time delay between the i^(th) transmit antennato the j^(th) receive antenna element, for i=1, 2, . . . , M and j=1, 2,. . . , N.
 3. The MIMO radar of claim 2, wherein the time delay τ_(ij)is defined as:${\tau_{ij} = {\frac{1}{c}d_{ij}{\sin\left( \theta_{i} \right)}}},$where d_(ij) a distance between the i^(th) element to a referenceelement, θ_(i) is the incident angle that is an angle between adirection of the incident signal received at the i^(th) element and thenormal that is perpendicular to a plane of the virtual receive array. 4.The MIMO radar of claim 3, wherein the incident angle is derived from apredetermined direction of arrival for each of the N receive subarraysthat constitute the virtual receive array.
 5. The MIMO radar of claim 1,wherein the DSP is further configured to apply a linear transformationmatrix with interpolation to the manifold matrix to generate an orientedvirtual subarray within the virtual receive array.
 6. The MIMO radar ofclaim 5, wherein the DSP is further configured to apply interpolation tosignals received by receive elements of the virtual receive array togenerate the oriented virtual subarray at a predetermined orientationangle.
 7. The MIMO radar of claim 1, wherein the DSP is furtherconfigured to calculate the manifold matrix by a least square algorithmwhen a size of the virtual receive array is smaller than the receiveantenna array.
 8. The MIMO radar of claim 1, wherein the DSP is furtherconfigured to: apply the linear transformation to first transmitantennas of the plurality of transmit antennas to determine secondtransmit antennas positioned at an angle relative to an originalposition of the first transmit antennas; and apply the lineartransformation to the receive antenna array to determine a secondreceive array at an angle relative to an original position of the firstreceive array, wherein the virtual receive array is spaced from thesecond receive antenna array by a same distance as that between thesecond transmit antennas.
 9. The MIMO radar of claim 1, wherein the DSPis further configured to perform linear transformations on the virtualreceive array to create virtual beam steering at a predetermined angle.10. The MIMO radar of claim 9, wherein the DSP is further configured tosend a control signal to the receive antenna array that causes one ormore receive beams to steer based at least on the virtual receive array.11. The MIMO radar of claim 1, wherein each transmit antenna of theplurality of transmit antennas is positioned at a given set ofcoordinates and are spaced within a relative distance of each other, andwherein the relative distance between each transmit antenna is smallerthan a wavelength that increases grating lobe immunity.
 12. The MIMOradar of claim 11, wherein the virtual receive array is spaced from thereceive antenna array by a same relative distance as that betweentransmit antennas of the plurality of transmit antennas.
 13. A method ofvirtual beam steering, comprising: synthesizing a virtual receive arrayhaving N×M receive subarrays from the plurality of transmit antennas andthe receive antenna array, where N is the number of transmit antennasand M is the number of receiving elements, wherein the virtual receivearray is represented by a manifold matrix that is a function of ageometry of the receive antenna array and a carrier frequency anddirection of arrival of the plurality of transmit antennas, and atransformation matrix is applied to the manifold matrix to generate thevirtual receive array; and performing a linear transformation on thevirtual receive array to create virtual beam steering at a predeterminedangle.
 14. The method of claim 13, further comprising: applying thelinear transformation to first transmit antennas of the plurality oftransmit antennas to determine second transmit antennas positioned at anangle relative to an original position of the first transmit antennas;and applying the linear transformation to the receive antenna array todetermine a second receive array at an angle relative to an originalposition of the first receive array, wherein the virtual receive arrayis spaced from the second receive antenna array by a same distance asthat between the second transmit antennas.
 15. The method of claim 13,further comprising: applying a linear transformation matrix withinterpolation to the manifold matrix to generate an oriented virtualsubarray within the virtual receive array.
 16. The method of claim 15,wherein applying the linear transformation matrix comprises: applyinginterpolation to signals received by receive elements of the virtualantenna array to generate the oriented virtual subarray at apredetermined orientation angle.
 17. The method of claim 13, furthercomprising: determining a transformation matrix from the manifoldmatrix; generating the virtual receive array from the transformationmatrix; determining a linear transformation matrix using an optimizationcriterion that is a function of the manifold matrix and thetransformation matrix applied to the manifold matrix; and generating adata set that represents beam steering properties using the determinedlinear transformation matrix and received signal samples.